class: center, middle, inverse, title-slide # Lecture 8 ## Multiple Groups ### Psych 10 C ### University of California, Irvine ### 04/15/2022 --- ## Comparisons between two groups - Let's look at another example of comparisons between two populations. -- - First we need a research problem or question. -- - We are interested in studying the levels of anxiety in first year students at a university in two different cohorts, the first one started in 2018 and the second one in 2019. -- - The University makes all students take a survey during the first week which includes a scale design to measure anxiety on a scale that goes from 0 to 20. -- - We have been granted access to the data of 30 students of each cohort to analize if there are any differences between the levels of anxiety. -- - Is this a paired samples (within subjects) design or an independent samples (between subjects) design? --- ## First year anxiety - Before we get the results, we want to formalize our models. -- - **Null model:** There are no difference in axiety levels between students in the 2018 cohort and students in the 2019 cohort. In other words, the axiety level of each student is an independent sample of the distribution: `$$y_{ij} \sim \text{Normal}(\mu,\sigma_0^2)$$` for `\(i=1,\dots,30\)` students and `\(j = 1, 2\)` where 1 represents that the student belongs to the 2018 cohort and 2 represents students of the 2019 cohort. -- - **Effects model:** The anxiety levels of students in the 2018 cohort are different from the levels of the 2019 cohort. In other words, the anxiety level of a student in group `\(j=1,2\)` where 1 denotes the 2018 cohort and 2 denotes 2019 are an independent sample of the distributions: `$$y_{ij} \sim \text{Normal}(\mu_j, \sigma_e^2)$$` for `\(i = 1,\dots,30\)` students.